/** ======================================================================* NIST Guide to Available Math Software.* Fullsource for module SSYEVX.C from package CLAPACK.* Retrieved from NETLIB on Fri Mar 10 14:23:44 2000.* ======================================================================*/#include <f2c.h>/* Subroutine */ int ssterf_(integer *n, real *d, real *e, integer *info){/*  -- LAPACK routine (version 2.0) --          Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,          Courant Institute, Argonne National Lab, and Rice University          September 30, 1994       Purpose       =======       SSTERF computes all eigenvalues of a symmetric tridiagonal matrix       using the Pal-Walker-Kahan variant of the QL or QR algorithm.       Arguments       =========       N       (input) INTEGER               The order of the matrix.  N >= 0.       D       (input/output) REAL array, dimension (N)               On entry, the n diagonal elements of the tridiagonal matrix.               On exit, if INFO = 0, the eigenvalues in ascending order.       E       (input/output) REAL array, dimension (N-1)               On entry, the (n-1) subdiagonal elements of the tridiagonal               matrix.               On exit, E has been destroyed.       INFO    (output) INTEGER               = 0:  successful exit               < 0:  if INFO = -i, the i-th argument had an illegal value               > 0:  the algorithm failed to find all of the eigenvalues in                     a total of 30*N iterations; if INFO = i, then i                     elements of E have not converged to zero.       =====================================================================          Test the input parameters.          Parameter adjustments          Function Body */    /* Table of constant values */    static integer c__0 = 0;    static integer c__1 = 1;    static real c_b32 = 1.f;        /* System generated locals */    integer i__1;    real r__1, r__2;    /* Builtin functions */    double sqrt(doublereal), r_sign(real *, real *);    /* Local variables */    static real oldc;    static integer lend, jtot;    extern /* Subroutine */ int slae2_(real *, real *, real *, real *, real *)	    ;    static real c;    static integer i, l, m;    static real p, gamma, r, s, alpha, sigma, anorm;    static integer l1, lendm1, lendp1;    static real bb;    extern doublereal slapy2_(real *, real *);    static integer iscale;    static real oldgam;    extern doublereal slamch_(char *);    static real safmin;    extern /* Subroutine */ int xerbla_(char *, integer *);    static real safmax;    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 	    real *, integer *, integer *, real *, integer *, integer *);    static integer lendsv;    static real ssfmin;    static integer nmaxit;    static real ssfmax;    extern doublereal slanst_(char *, integer *, real *, real *);    extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *);    static integer lm1, mm1, nm1;    static real rt1, rt2, eps, rte;    static integer lsv;    static real tst, eps2;#define E(I) e[(I)-1]#define D(I) d[(I)-1]    *info = 0;/*     Quick return if possible */    if (*n < 0) {	*info = -1;	i__1 = -(*info);	xerbla_("SSTERF", &i__1);	return 0;    }    if (*n <= 1) {	return 0;    }/*     Determine the unit roundoff for this environment. */    eps = slamch_("E");/* Computing 2nd power */    r__1 = eps;    eps2 = r__1 * r__1;    safmin = slamch_("S");    safmax = 1.f / safmin;    ssfmax = sqrt(safmax) / 3.f;    ssfmin = sqrt(safmin) / eps2;/*     Compute the eigenvalues of the tridiagonal matrix. */    nmaxit = *n * 30;    sigma = 0.f;    jtot = 0;/*     Determine where the matrix splits and choose QL or QR iteration          for each block, according to whether top or bottom diagonal          element is smaller. */    l1 = 1;    nm1 = *n - 1;L10:    if (l1 > *n) {	goto L170;    }    if (l1 > 1) {	E(l1 - 1) = 0.f;    }    if (l1 <= nm1) {	i__1 = nm1;	for (m = l1; m <= nm1; ++m) {	    tst = (r__1 = E(m), dabs(r__1));	    if (tst == 0.f) {		goto L30;	    }	    if (tst <= sqrt((r__1 = D(m), dabs(r__1))) * sqrt((r__2 = D(m + 1)		    , dabs(r__2))) * eps) {		E(m) = 0.f;		goto L30;	    }/* L20: */	}    }    m = *n;L30:    l = l1;    lsv = l;    lend = m;    lendsv = lend;    l1 = m + 1;    if (lend == l) {	goto L10;    }/*     Scale submatrix in rows and columns L to LEND */    i__1 = lend - l + 1;    anorm = slanst_("I", &i__1, &D(l), &E(l));    iscale = 0;    if (anorm > ssfmax) {	iscale = 1;	i__1 = lend - l + 1;	slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &D(l), n, 		info);	i__1 = lend - l;	slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &E(l), n, 		info);    } else if (anorm < ssfmin) {	iscale = 2;	i__1 = lend - l + 1;	slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &D(l), n, 		info);	i__1 = lend - l;	slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &E(l), n, 		info);    }    i__1 = lend - 1;    for (i = l; i <= lend-1; ++i) {/* Computing 2nd power */	r__1 = E(i);	E(i) = r__1 * r__1;/* L40: */    }/*     Choose between QL and QR iteration */    if ((r__1 = D(lend), dabs(r__1)) < (r__2 = D(l), dabs(r__2))) {	lend = lsv;	l = lendsv;    }    if (lend >= l) {/*        QL Iteration             Look for small subdiagonal element. */L50:	if (l != lend) {	    lendm1 = lend - 1;	    i__1 = lendm1;	    for (m = l; m <= lendm1; ++m) {		tst = (r__1 = E(m), dabs(r__1));		if (tst <= eps2 * (r__1 = D(m) * D(m + 1), dabs(r__1))) {		    goto L70;		}/* L60: */	    }	}	m = lend;L70:	if (m < lend) {	    E(m) = 0.f;	}	p = D(l);	if (m == l) {	    goto L90;	}/*        If remaining matrix is 2 by 2, use SLAE2 to compute its             eigenvalues. */	if (m == l + 1) {	    rte = sqrt(E(l));	    slae2_(&D(l), &rte, &D(l + 1), &rt1, &rt2);	    D(l) = rt1;	    D(l + 1) = rt2;	    E(l) = 0.f;	    l += 2;	    if (l <= lend) {		goto L50;	    }	    goto L150;	}	if (jtot == nmaxit) {	    goto L150;	}	++jtot;/*        Form shift. */	rte = sqrt(E(l));	sigma = (D(l + 1) - p) / (rte * 2.f);	r = slapy2_(&sigma, &c_b32);	sigma = p - rte / (sigma + r_sign(&r, &sigma));	c = 1.f;	s = 0.f;	gamma = D(m) - sigma;	p = gamma * gamma;/*        Inner loop */	mm1 = m - 1;	i__1 = l;	for (i = mm1; i >= l; --i) {	    bb = E(i);	    r = p + bb;	    if (i != m - 1) {		E(i + 1) = s * r;	    }	    oldc = c;	    c = p / r;	    s = bb / r;	    oldgam = gamma;	    alpha = D(i);	    gamma = c * (alpha - sigma) - s * oldgam;	    D(i + 1) = oldgam + (alpha - gamma);	    if (c != 0.f) {		p = gamma * gamma / c;	    } else {		p = oldc * bb;	    }/* L80: */	}	E(l) = s * p;	D(l) = sigma + gamma;	goto L50;/*        Eigenvalue found. */L90:	D(l) = p;	++l;	if (l <= lend) {	    goto L50;	}	goto L150;    } else {/*        QR Iteration             Look for small superdiagonal element. */L100:	if (l != lend) {	    lendp1 = lend + 1;	    i__1 = lendp1;	    for (m = l; m >= lendp1; --m) {		tst = (r__1 = E(m - 1), dabs(r__1));		if (tst <= eps2 * (r__1 = D(m) * D(m - 1), dabs(r__1))) {		    goto L120;		}/* L110: */	    }	}	m = lend;L120:	if (m > lend) {	    E(m - 1) = 0.f;	}	p = D(l);	if (m == l) {	    goto L140;	}/*        If remaining matrix is 2 by 2, use SLAE2 to compute its             eigenvalues. */	if (m == l - 1) {	    rte = sqrt(E(l - 1));	    slae2_(&D(l), &rte, &D(l - 1), &rt1, &rt2);	    D(l) = rt1;	    D(l - 1) = rt2;	    E(l - 1) = 0.f;	    l += -2;	    if (l >= lend) {		goto L100;	    }	    goto L150;	}	if (jtot == nmaxit) {	    goto L150;	}	++jtot;/*        Form shift. */	rte = sqrt(E(l - 1));	sigma = (D(l - 1) - p) / (rte * 2.f);	r = slapy2_(&sigma, &c_b32);	sigma = p - rte / (sigma + r_sign(&r, &sigma));	c = 1.f;	s = 0.f;	gamma = D(m) - sigma;	p = gamma * gamma;/*        Inner loop */	lm1 = l - 1;	i__1 = lm1;	for (i = m; i <= lm1; ++i) {	    bb = E(i);	    r = p + bb;	    if (i != m) {		E(i - 1) = s * r;	    }	    oldc = c;	    c = p / r;	    s = bb / r;	    oldgam = gamma;	    alpha = D(i + 1);	    gamma = c * (alpha - sigma) - s * oldgam;	    D(i) = oldgam + (alpha - gamma);	    if (c != 0.f) {		p = gamma * gamma / c;	    } else {		p = oldc * bb;	    }/* L130: */	}	E(lm1) = s * p;	D(l) = sigma + gamma;	goto L100;/*        Eigenvalue found. */L140:	D(l) = p;	--l;	if (l >= lend) {	    goto L100;	}	goto L150;    }/*     Undo scaling if necessary */L150:    if (iscale == 1) {	i__1 = lendsv - lsv + 1;	slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &D(lsv), n, 		info);    }    if (iscale == 2) {	i__1 = lendsv - lsv + 1;	slascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &D(lsv), n, 		info);    }/*     Check for no convergence to an eigenvalue after a total          of N*MAXIT iterations. */    if (jtot == nmaxit) {	i__1 = *n - 1;	for (i = 1; i <= *n-1; ++i) {	    if (E(i) != 0.f) {		++(*info);	    }/* L160: */	}	return 0;    }    goto L10;/*     Sort eigenvalues in increasing order. */L170:    slasrt_("I", n, &D(1), info);    return 0;/*     End of SSTERF */} /* ssterf_ */